Every Once in a While...

I cannot recommend this highly enough: have your kids bring in questions for you to answer in class. 

As I mentioned in the last post, I asked my kids to do this, and this week they responded with some really great questions, most of which I had never seen or tried to solve before.

I gave each problem about 5 minutes of time in class, just thinking through it out loud, trying an idea or two to see where it would lead. For a few of the problems the initial idea was fruitful and I was able to solve on the spot in class.  For others, the initial idea was off the mark and I needed to start over and try something else.  I think the kids enjoyed watching me squirm a bit too much on these, but in a way the whole point was for them to see me struggle, be wrong, try again, make a silly arithmetic mistake, go back to an idea that had been previously discarded, and so on.  And for a couple of the problems, I needed to take it home and work it through that evening, returning with an answer the following day.

I wasn’t able to take a problem every day in every class, just because of other things going on (a tornado drill on one day, for example), but I was able to do so a couple times in each class, and by the looks of it they got the point.  A few kids told me outright that they got a lot out of the discussion around these questions.  Also, there was a little more “I’m not sure if I’m right, but I’ll put what I’ve got on the board” by the end of the week.  By seeing me be imperfect right there in front of them, there was a little more understanding that I’m not looking for them to be perfect, but instead I’m looking for them to learn from their imperfections.  And by the end of the week, one of the first statements made in each class as the kids were walking in was, “I’ve got a questions for you to try today,” so if nothing else I know that the kids are enjoying the discussion and that we have at least a couple more weeks’ worth of exercises ready. 

One of the students was intrigued enough by one of the problems that we had a short conversation on Twitter about it that evening, which for me was one of the highlights of the week: a student doing math for the sake of solving the puzzle and for the learning, and more importantly not for the sake of the grade.  It also got me thinking about possibly putting a student-posed problem of the week online for the kids to discuss, just for the sake of having the discussion.  The difficulty, of course, is that communicating mathematics online is cumbersome, at best, but it may be worth the try to see what creative ways the kids come up with to overcome the difficulty.

Another thought that crossed my mind was that this idea would have merit in other disciplines.  Having students bring in a poem for the teacher to analyze in English class, an article for the teacher to translate in Spanish class, or a document for the teacher to explore in history class would be a great exercise for both the teacher and the students, as would the resulting discussions.

So, nothing but a positive update to last week’s post.  Nice to have this happen every once in a while.

Leading by Example

It occurred to me this week that for as much as we tell the kids to not be afraid of making mistakes (so long as they learn from them) and convince them that problem solving is actually a pretty messy process, we don’t dare go into a class without having meticulously worked the exercises ourselves so that any struggle on our part is hidden from view.  The kids never get to see us actually do any real problem solving.  They never get to see us actually work our way through a problem we haven’t seen before.  We may think we’re demonstrating the process at times, but truth be told we never actually model the process for them.

That ends tomorrow in my classroom.

I have asked the students in my honors pre-calculus classes to bring in a math problem for me to solve.  Any math problem.  I gave them fair warning that if they wanted to see me work the problem all the way through then they would need to make sure the problem was “reasonable”.  However, I also told them that regardless of what they brought in, there would be merit in me making an attempt at it, as they would get to see how to begin to attack a problem when they have no idea where to start.

Yes, I may have just set myself up to face plant onto the tile of my classroom.  Yes, they may bring in something that I will have no idea where to begin.  Yes, they might just get to see me make a mistake or five.  And that’s the point.  If I’m asking them to get comfortable with making mistakes in front of the class, then I need to show them that I’m comfortable making mistakes in front of them.  If I’m asking them to at least make an attempt on a problem, then I need to do the same right there in front of them.  If I’m asking them to admit that they’re human, then I need to admit the same.

Honestly, I’m interested to see what they bring in.  I’m excited for the challenge.  I’m looking forward to displaying my love for the subject and for the “puzzle” that, for me, is what mathematics is all about.  And if I mess up, that’s ok.  The kids will be able to learn at least as much from that, and possibly more, than if I am able to solve the problem on the first try.

I’ll report how things turned out next week.

Stage Two

I’m now a few weeks into the next phase of infusing discussion-based learning into my classroom. Specifically, I’m teaching a section of college-prep algebra 1 this year, and so far, I’ve not needed to lecture much at all.  Every few days or so I will summarize what we’ve been doing, or if there is a topic that I know from experience kids find confusing (like function notation) then I will spend a few minutes dealing specifically with that topic.  Other than that, I have been creating worksheets for each section, much in the same way I did a few years ago when we did the “test run” with Harkness in the conics unit of honors pre-calculus.  Put simply, I look at the section, determine how I would lecture on the section, and then I create a list of questions that (hopefully) lead the kids through the material.  Instead of putting examples on the board and going through them, I take a little more care in scaffolding the examples, creating them in such a way that the kids can at least begin if not complete the examples themselves, discuss their results in a group, and through this process learn the material.

So far, things are going well.  Half the class earned an “A” on the first “individual exercise set” (it sounds less threatening than “test”), and for the most part those that didn’t made simple arithmetic mistakes as opposed to making fundamental algebra mistakes.  Moving into the second unit, things are going equally well, and the kids are getting a lot out of the discussions.  A few haven’t “bought in” yet, and while I’m still trying to get them on board, I don’t believe that the class being run through discussion is the reason for their lack of effort.  Rather, they appear to be genuinely disengaged from school in general, which is a far taller wall in my way when it comes to reaching them.  Even an activity we did last week (“So, how many standard-sized Post-It notes would it take to cover the walls of the classroom, except for the white boards?”) didn’t catch them.  The rest of the class was up, making different measurements they thought would be useful, and worked hard on the exercise for 30+ minutes.  The other few just sat at their desk, waiting for the rest of the group to give them the answer.  Talking with them, encouraging them, trying to get them to participate…nothing worked.  It’s really sort of sad to see that the natural curiosity that fills kids when they are young has been essentially removed from these kids.  What it is that deadened the natural curiosity can vary, and part of my role is to help them through that, whatever “that” is.  Still sad, though.

Anyway, in general I’m happy with the results so far and am optimistic that things will continue going well.  If nothing else, these first few weeks of the year have convinced me that discussion-based learning isn’t just for honors kids, nor is it just for upper-level material; it is working well with college-prep freshmen.  Hopefully, I will find a way to get the few holdouts to join the rest of us in learning some math in a slightly more relaxed manner than they’re used to.